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we know in this game that β is dominated, is strictly dominated by α.
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It's something that we learned the very first time.
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Just to check: so against α,
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choosing α gets you 0, β gets you -1.
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Against β choosing α Gets you 3, β gets you 1,
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and in either case α is strictly better, so α strictly dominates β,
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and of course it's the same for the column player
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since the game's completely symmetric.
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So now, let's find the Nash Equilibrium in this game.
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I think we know what it's going to be,
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but let's just do it in this sort of slow way.
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So, the best response to α must be α.